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Warm Up Introduction to Polynomials and Adding and Subtracting Polynomials

Warm Up Introduction to Polynomials and Adding and Subtracting Polynomials. Classifying Polynomials:. We classify polynomials based on the number of _________. terms. What is a monomial?. A polynomial with only 1 term. What is a binomial?. A polynomial with 2 terms.

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Warm Up Introduction to Polynomials and Adding and Subtracting Polynomials

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  1. Warm UpIntroduction to Polynomials and Adding and Subtracting Polynomials

  2. Classifying Polynomials: We classify polynomials based on the number of _________. terms What is a monomial? A polynomial with only 1 term. What is a binomial? A polynomial with 2 terms. A polynomial with 3 terms. What is a trinomial? When do we use the term polynomial? We use the term polynomial to describe any expression which contains some combination of variables and numbers.

  3. What is a term? Terms are made up of numbers, variables or the product and/or quotient of some combination of numbers and variables. EXAMPLE: 2x is a term. (the product of a # and variable) 2x/3 is a term. (the quotient of a # and variable) - + Terms are separated by ________ and ________ signs!

  4. Classify each of the polynomials • 3x2y + 3x + 4y • 2x2y4z • 2xy2 + 3x2y + 9x • 5x2y + 2xy3 Trinomial Monomial Trinomial Binomial

  5. Calculating the degree of a polynomial.. If it is a single variable term, find the term with the largest exponent. 5x3 + 9x2 + x This is a 3rd degree polynomial. 1 Remember the understood 1!!! If it is a multi-variable term, you add the exponents of all of the variables. 4x2y + 2xy3 + 9 This is a 4th degree polynomial (3+1=4). Don’t forget the understood 1’s!!!! 1 1

  6. Calculate the degree of the polynomial… • 6x2 + 4x + 4x3 + x • 21x2y + 12x4y2 + 2xy4 • 3x2 + 2y3 3rd degree 6th degree 3rd degree

  7. Writing a polynomial in standard form… • Standard form is in descending order of the x variable. • 2xy3 + 3x2y + x3 • 3xy2 + 3x3 + 2x2y X3 + 3x2y + 2xy3 3x3 + 2x2y + 3xy2

  8. Adding and Subtracting Polynomials… is nothing more than combining like terms. Remember you can do this vertically or horizontally. • (2x2 - 3x + 3) + (4x2 + 5x - 9) • (3x2 - 9x - 5) - (-2x2 - 4x + 5) 6x2 + 2x -6 5x2 - 5x - 10 5(x2 - x - 2)

  9. Ex 1 (x2 + 3x + 4) + (-2x2 + 10x - 5) Combine LIKE terms x2 + 3x + 4 -2x2 + 10x - 5 -1x2 + 13x - 1 Final Answer

  10. Ex 2. (4b3 - 2b) + (b3 + 6b2 + 3b - 7) 4b3 + 0b2 - 2b + 0 b3 + 6b2 + 3b - 7 5b3 + 6b2 + 1b - 7 Final Answer

  11. Ex 3. (12y2 - 8y + 4) - (9y2 + 5y + 1) Don’t forget to Distribute the -1!! (12y2 - 8y + 4) - 1(9y2 + 5y + 1) (12y2 - 8y + 4) - 9y2- 5y - 1 12y2 - 8y + 4 - 9y2- 5y - 1 3y2 - 13y + 3 Final Answer

  12. Ex 4. (3a3 + 10a - 15) - (-a3 + 2a2 + 6a - 9) (3a3 + 10a - 15) - 1(-a3 + 2a2 + 6a - 9) 3a3 + 10a - 15 + a3 - 2a2- 6a + 9 3a3 + 0a2 + 10a - 15 +a3 - 2a2 - 6a + 9 4a3 - 2a2 + 4a - 6 Final Answer

  13. POLYNOMIAL MULTIPLICATION (2x - 3)(x + 5) 3 methods • Distribute (2x - 3)(x + 5) *4 multiplications 2x2+ 10x- 3x - 15 (then combine like terms) 2x2+ 10x - 3x - 15 2x2 + 7x - 15 Final Answer

  14. b. 3rd grade style 2x - 3 x + 5 +10x - 15 2x2 - 3x + 0 2x2 + 7x - 15 Final Answer!

  15. c. Box Method 2x - 3 x 2x2-3x + 5 +10x -15 2x2 + 7x - 15 Final Answer

  16. Ex 5. (4x + 7)(3x + 7) a.) 12x2+ 28x+ 21x + 49 12x2 + 49x + 49 b.) 4x + 7 c.) 4x + 7 3x + 7 3x 12x2 +21x +28x + 49 + 7 +28x + 49 12x2 + 21x + 0 12x2 + 49x + 49

  17. Ex 6. (x - 1)(x2 - 4x + 6) • x3- 4x2+ 6x - 1x2+ 4x- 6 x3 - 5x2 + 10x - 6 b. x2 - 4x + 6 c. x2 - 4x + 6 x - 1 x x3 -4x2 +6x -1x2 + 4x - 6 -1 -1x2 +4x - 6 1x3 -4x2 + 6x + 0 x3 - 5x2 + 10x - 6 x3 - 5x2 + 10x - 6

  18. Ex 7. (2z2 + 3z - 4)(4z + 5) • 8z3+ 10z2+ 12z2 + 15z - 16z- 20 8z3 + 22z2 - 1z - 20 b. 2z2 + 3z - 4 c. 2z2 + 3z - 4 4z + 5 4z 8z3 +12z2 -16z +10z2 + 15z - 20 +5 10z2 +15z - 20 8z3 +12z2 - 16z + 0 8z3 + 22z2 - 1z - 20

  19. Ex 8. (2a + 5)(2a - 5) • 4a2- 10a+ 10a - 25 4a2 - 25 b. 2a + 5 c. 2a +5 2a - 5 2a 4a2 +10a -10a - 25 -5 -10a -25 4a2 +10a + 0 4a2 - 25 4a2 - 25

  20. Ex 9. (3m + 4n)2 • (3m + 4n)(3m + 4n) 9m2+ 12mn+ 12mn + 16n2 9m2 + 24mn + 16n2 b. 3m + 4n c. 3m +4n 3m + 4n 3m 9m2 +12mn +12mn + 16n2 +4n +12mn +16n2 9m2 + 12mn + 0 9m2 + 24mn + 16n2 9m2 + 24mn + 16n2

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